Yes you can, providing you have a Personal Public Service Number (PPSN). A PPSN is an explicit requirement for purchasing Ireland State Savings products. 

If you do not have a PPSN and want to see if you are eligible to get one, you can apply to the Department of Employment Affairs and Social Protection. Ireland State Savings cannot advise on the requirements and/or process in regard to applications for PPSN.

Foreign Tax Identification Numbers are not accepted by Ireland State Savings.